NSF Young Investigator Award

这项研究解决了机器感知和机器人学中的问题。这项工作主要集中在两个领域：识别图像中的曲线对象，以及移动机器人导航。识别图像特征强烈依赖于视点的复杂曲面三维物体是计算机视觉的基本问题之一。对象由代数曲面及其相交曲线的集合来建模，预测和解释这些模型的图像所涉及的几何约束由多项式约束集来表示。可以使用代数几何和稳健数值方法中的技术来解决这些约束。视点相关特征是从对象模型预测的，并被表示为一个方面图，该图列举了所有拓扑上不同的视图。消元理论被用来将图像测量与对象联系起来，并且可以应用优化技术来估计对象的姿势；然后从模型库中识别对象。需要解决的问题包括对象模型的自动生成、新的对象表示法、有限分辨率传感器的预测、计算效率以及索引大型数据库。移动机器人为非结构化世界中健壮的计算机视觉算法提供了一个动态的试验台。除了开发新的传感器外，研究的重点是获得执行任务所需的信息。虽然一些活动很容易通过视觉服务实现，但其他活动需要开发环境的3D表示。立体声和运动结构提供来自图像测量的3D信息，这些信息可以合并到关系地图中。这张地图构成了运动规划的基础；可以确定重访以前看到的地方的路径和探索新区域的策略。此外，当该地图中的对象被识别时，机器人任务和文化约束被更自然地描述。

This research addresses problems in machine perception and robotics. The work is focused in two areas: recognizing curved objects in images, and mobile robot navigation. Recognizing complex curved 3D objects, whose image features depend strongly on viewpoint, is one of the fundamental problems of computer vision. Objects are modelled by collections of algebraic surfaces and their intersection curves, and the geometric constraints involved in predicting and interpreting the images of these models are represented by sets of polynomial constraints. Techniques from algebraic geometry and robust numerical methods can be used to solve these constraints. Viewpoint dependent features are predicted from an object model and represented as an aspect graph which enumerates all topologically distinct views. Elimination theory is used to relate image measurements to objects, and optimization techniques can be applied to estimate an object's pose; objects are then recognized from a library of models. Problems to be addressed include automatic generation of object models, new object representations, prediction for sensors with limited resolution, computational efficiency, and indexing large data bases. Mobile robots provide a dynamic test-bed for robust computer vision algorithms in an unstructured world. In addition to developing new sensors, research focuses on obtaining the necessary information to perform a task. While some activities are readily achieved through visual serving, others require developing a 3D representation of the environment. Stereo and structure-from-motion provide 3D information from image measurements which can be incorporated into a relational map. This map forms the basis for motion planning; paths revisit previously seen places and strategies for exploring new areas can be determined. Additionally, robot tasks and cultural constraints are described more naturally when objects are recognized within this map.